SOLUTION: A man walks 25 miles a day. On the following days he travel 5% less each day than the previous day. If he walked in the straight line, how far from his statrting point would he tra

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Question 242174: A man walks 25 miles a day. On the following days he travel 5% less each day than the previous day. If he walked in the straight line, how far from his statrting point would he travel?
I'm learning infinite geometric series, please explain your solutions. Thanks for your helps.
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A man walks 25 miles a day. On the following days he travel 5% less each day than the previous day. If he walked in the straight line, how far from his starting point would he travel?
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The series is 25 + (0.95)(25) + (0.95)^2(25) +...
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This is a geometric series with
a = 25 and r = 0.95
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Infinite Sum = a[1/(1-r)] = 25[1/0.05] = 500 miles
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Cheers,
Stan H.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


If he travels 5% less distance each day, then he travels 95% of the previous days distance. Hence the common ratio is 95%, or .95.

The sum of the infinite series:



Just plug in your values:



Now all you need to do is a little arithmetic.


John